The formation of two-component multilayer films on solid surfaces in the systems of adsorbates, which exhibit positive deviations from ideal mixing, is studied using a Monte Carlo simulation method. Phase behaviour of the systems exhibiting complete and incomplete wetting at the ground state is discussed. Phase diagrams for several systems are determined. It is demonstrated that the systems studied exhibit strong effects of enhanced adsorption of one component due to adsorption of the second component. It is also shown that the presence of preadsorbed particles of one component may considerably change the surface wetting by the second component. In particular, it is demonstrated that the addition of strongly adsorbed particles into the system may lead to the cross-over from the intermediate to the strong substrate regime. On the other hand, in the systems considered here the wetting temperature appears to be practically unaffected by the second component. When the wetting transition is preceded by the (first-order) prewetting transition, its critical point, is shifted towards higher temperatures due to the enhancement of adsorbate-adsorbate interaction resulting from the enhanced adsorption of the second component.